where \(\kappa \)  is a scaling factor for the fine tuning of the higher order moments of the approximation error [1]}. How to tune the value of \(\kappa \)  for a sparsity-based UKF is an open problem that needs further study. In this paper, \(\kappa =0\)  is used in all examples. A set of \(\sigma \) -points is generated as follows,
\(\begin{array}{lllllllll}x^\sigma _0(k-1)=x^a (k-1),\\x^\sigma _i(k-1)=x^a(k-1)+X^a_i(k-1), & 1\le i\le n, \\x^\sigma _i(k-1)=x^a(k-1)-X^a_i(k-1), & n+1\le i\le 2n. \\\end{array}\) 
